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Wavelets XI

作者： Maggioni, Mauro Bremer Jr., James C. Coifman, Ronald R. Szlam, Arthur D. Department of Mathematics Program in Applied Mathematics Yale University 10 Hillhouse Ave New Haven CT 06520

Recent work by some of the authors presented a novel construction of a multiresolution analysis on manifolds and graphs, acted upon by a given symmetric Markov semigroup {Tt}t≥o, for which T t has low rank for large t.1 This includes important classes of diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. The dyadic powers of an operator are used to induce a multiresolution analysis, analogous to classical Littlewood-Paley14 and wavelet theory, while associated wavelet packets can also be constructed.2 This extends multiscale function and operator analysis and signal processing to a large class of spaces, such as manifolds and graphs, with efficient algorithms. Powers and functions of T (notably its Green's function) are efficiently computed, represented and compressed. This construction is related and generalizes certain Fast Multipole Methods, 3 the wavelet representation of Calderón-Zygmund and pseudo-differential operators,4 and also relates to algebraic multigrid techniques.5 The original diffusion wavelet construction yields orthonormal bases for multiresolution spaces {Vj}. The orthogonality requirement has some advantages from the numerical perspective, but several drawbacks in terms of the space and frequency localization of the basis functions. Here we show how to relax this requirement in order to construct biorthogonal bases of diffusion scaling functions and wavelets. This yields more compact representations of the powers of the operator, better localized basis functions. This new construction also applies to non self-adjoint semigroups, arising in many applications.

关键词： Wavelet transforms

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TWO ALGORITHMS FOR LC^1 UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2000年第6期18卷 621-632页

作者： Wen-yu Sun R.J.B.de Sampaio Jin-Yun Yuan School of Mathematics and Computer Science Nanjing Normal UniversityNanjing 210097China Applied Informatics Program Pontifical Catholic University of ParanaCuritibaPR81611-970Brazil Department of Mathematics Federal University of ParanaCuritibaPR81531-990Brazil

Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it... 详细信息

关键词： nonsmooth optimization directional derivative Newton-like method convergence trust region method

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Mean field limit of a dynamical model of polymer systems

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Science China mathematics 2013年第12期56卷 2591-2598页

作者： E Weinan SHEN Hao School of Mathematical Sciences and BICMR Peking University Department of Mathematics and PACM Princeton UniversityPrinceton NJ 08544 USA Program in Applied and Computational Mathematics Princeton UniversityPrinceton NJ 08544 USA

This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.

关键词： polymers mean field limit stochastic PDEs McKean-Vlasov equation

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Motor cortex repetitive transcranial magnetic stimulation in fibromyalgia: a multicentre randomised controlled trial

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British Journal of Anaesthesia 2025年第6期134卷 1756-1764页

作者： Silva, Valquíria A. Baptista, Abrahão F. Fonseca, Alessandra S. Carneiro, Adriana M. Brunoni, André R. Carrilho, Paulo.E.M. Lins, Catarina C. Kubota, Gabriel T. Fernandes, Ana Mércia B.L. Lapa, Jorge.D.S. dos Santos, Lucas M. Sasso, Ivo Monte-Silva, Katia Poindessous-Jazat, Frédérique Mori, Nobuhiko Miki, Kenji Baltar, Adriana Tanaka, Clarice Teixeira, Manoel J. Hosomi, Koichi Bouhassira, Didier Attal, Nadine Ciampi de Andrade, Daniel LIM 62 - Pain Center Department of Neurology São Paulo Brazil Service of Interdisciplinary Neuromodulation (SIN) Department and Institute of Psychiatry São Paulo Brazil Medical-Surgical Nursing Department University of São Paulo São Paulo Brazil Center for Mathematics Computation and Cognition Federal University of ABC São Paulo Brazil Mood Disorder Program (Pro-GRUDA) Department of Psychiatry University of São Paulo São Paulo Brazil Medicine School “Professor Orival Alves” State University of Western Paraná (UNIOESTE) Paraná Brazil Neurosurgery Unit Hospital de Cirurgia Sergipe Aracaju Brazil Department of Medicine Federal University of Sergipe Sergipe São Cristóvão Brazil LIM 54 - Physiotherapy Research Laboratory University of São Paulo São Paulo Brazil Applied Neuroscience Laboratory Universidade Federal de Pernambuco Cidade Universitária Pernambuco Brazil UVSQ-Paris-Saclay University Ambroise Paré Hospital Boulogne-Billancourt U987 France Department of Neurosurgery Osaka University Graduate School of Medicine Osaka Japan Faculty of Health Science Osaka Yukioka College of Health Science Osaka Japan Center for Pain Management Hayaishi Hospital Osaka Japan Center for Neuroplasticity and Pain (CNAP) Department of Health Science and Technology University of Aalborg Gistrup Denmark

Background: Despite affecting 2–4% of the population worldwide, fibromyalgia often remains refractory to treatment. Here we report the first international randomised double-blind, sham-controlled trial developed to assess the efficacy of repetitive transcranial magnetic stimulation (rTMS) as an add-on therapy for fibromyalgia. Methods: Women aged ≥18 yr with fibromyalgia refractory to best available treatment were enrolled in Brazil, France, and Japan, and randomised to 10 Hz motor cortex (M1) rTMS, 3000 pulses day⁻¹, or sham stimulation. This included 10 induction sessions over 2 weeks, followed by weekly maintenance (6 weeks), and fortnightly extended maintenance (8 weeks). Primary outcome was ≥50% pain reduction at week 8 compared with baseline. Secondary outcomes included pain interference, mood, global impression of change, and Fibromyalgia Impact Questionnaire (FIQ) scores at weeks 8 and 16. Results: We randomised 101 women (mean age 48 [range 25-83] yr) into active (n=52) or sham (n=49) arms. Bayesian analysis revealed a 99.4% probability of ≥50% pain reduction at week 8 in the active group vs sham (odds ratio [OR] 3.04;95% credible interval [95% CrI] 1.26–8.06), with a number needed to treat of 4.54. Frequentist analysis confirmed that relative pain reduction was higher in the active than in the sham group (40.4% vs 18.4%, P=0.028). At week 16, this probability reduced to 34.2% (OR 0.815;95% CrI 0.313–2.1), but the likelihood of FIQ score reduction was 79.1%. The intervention appeared safe. Conclusions: Add-on M1-repetitive transcranial magnetic stimulation reduced pain intensity up to 8 weeks in women with fibromyalgia. Although analgesic effects waned, functional improvements remained during extended maintenance at week 16. © 2025 The Authors

关键词： chronic pain clinical trial fibromyalgia neuromodulation transcranial magnetic stimulation

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Multidimensional Hyperbolic Problems and Computations 1

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丛书名： The IMA Volumes in mathematics and its Applications

1000年

作者： James Glimm Andrew J. Majda

ISBN: (数字)9781461391210

ISBN: (纸本)9781461391234

This IMA Volume in mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

关键词： Analysis

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BPS2025 - Learning the conformational ensemble from cryo-EM

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Biophysical Journal 2025年第3期124卷 310a-310a页

作者： Jeffrey Xiang Jake Moomaw Kawamura Diego Sanchez Joshua Rhodes Erik H. Thiede Department of Chemistry and Chemical Biology Cornell University Ithaca NY USA Biophysics Program Cornell University Ithaca NY USA Center for Applied Mathematics Cornell University Ithaca NY USA

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Delay performance under the joint scheduling over Gilbert-Elliot channel

Delay performance under the joint scheduling over Gilbert-El...

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2006 Wireless Telecommunications Symposium, WTS

作者： Ishizaki, Fumio Hwang, Gang Uk Department of Mathematics Telecommunication Mathematics Research Center Korea University Division of Applied Mathematics and Telecommunication Engineering Program Korea Advanced Institute of Science and Technology

ISBN: (纸本)1424400465

In this paper, we consider a joint scheduling algorithm which is a combination of Knopp and Humblet (KH) scheduling, which fully exploits multiuser diversity, and round-robin (RR) scheduling, which does not use multiuser diversity at all. By assuming that the wireless channel process for each user is described by Gilbert-Elliot channel model, we develop a formula to estimate the tail distribution of packet delay for an arbitrary user under the joint scheduling. Numerical results exhibit that under the joint scheduling, the ratio of the number of slots assigned for the RR scheduling to that for the KH scheduling dominates the delay performance. © 2006 IEEE.

关键词： Scheduling

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Generalization and Memorization: The Bias Potential Model 2

Generalization and Memorization: The Bias Potential Model

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2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Yang, Hongkang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and PACM Princeton University United States

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges. © 2021 H. Yang & W. E.

关键词： Probability distributions

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Absolute change pivot rule for the simplex algorithm

Absolute change pivot rule for the simplex algorithm

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International MultiConference of Engineers and Computer Scientists, IMECS 2014

作者： Chankong, Kittiphong Intiyot, Boonyarit Sinapiromsaran, Krung Applied Mathematics and Computational Science Program Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9789881925336

The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.

关键词： Linear programming

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mathematics for cryo-electron microscopy

Mathematics for cryo-electron microscopy

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2018 International Congress of Mathematicians, ICM 2018

作者： Singer, Amit Department of Mathematics Program in Applied and Computational Mathematic Princeton University United States

ISBN: (纸本)9789813272934

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM. © ICM *** rights reserved.

关键词： X ray crystallography

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